%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:46:50 PM UTC 2026
% Result : Theorem 3.01s 1.26s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 17 unt; 2 def)
% Number of atoms : 154 ( 22 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 138 ( 57 ~; 55 |; 20 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 85 !; 4 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorbtion_for_intersection) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] : intersection(X0,union(X0,X1)) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f20]) ).
fof(f25,plain,
sK2 != intersection(sK2,union(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
sK2 != intersection(sK2,union(sK2,sK3)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
intersection(sK2,union(sK2,sK3)) != sK2,
inference(cnf_transformation,[],[f45]) ).
tcf(c_341,definition,
iPr_def_10 = union(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_342,definition,
iPr_def_11 = intersection(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_343,negated_conjecture,
iPr_def_11 != sK2,
inference(demodulation,[status(thm)],[c_66,c_341,c_342]) ).
tcf(c_554,plain,
intersection(iPr_def_10,sK2) = iPr_def_11,
inference(demodulation,[status(thm)],[c_342,c_59]) ).
tcf(c_563,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_341,c_49]) ).
tcf(c_598,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_554,c_54]) ).
tcf(c_661,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK2) ),
inference(superposition,[status(thm)],[c_61,c_598]) ).
tcf(c_698,plain,
subset(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_661,c_60]) ).
tcf(c_703,plain,
( ( iPr_def_11 = sK2 )
| ~ subset(iPr_def_11,sK2)
| ~ subset(sK2,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_733,plain,
( ( sK2 = iPr_def_11 )
| ~ subset(sK2,iPr_def_11) ),
inference(superposition,[status(thm)],[c_698,c_55]) ).
tcf(c_756,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_554,c_52]) ).
tcf(c_908,plain,
~ subset(sK2,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_733,c_343,c_698,c_703]) ).
tcf(c_974,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_756,c_563,c_756]) ).
tcf(c_981,plain,
! [X0: $i] :
( subset(sK2,X0)
| member(sK0(sK2,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_61,c_974]) ).
tcf(c_1027,plain,
subset(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_981,c_60]) ).
tcf(c_1030,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1027,c_908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 10:07:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.01/1.26 % SZS status Started for theBenchmark.p
% 3.01/1.26 % SZS status Theorem for theBenchmark.p
% 3.01/1.26
% 3.01/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.01/1.26
% 3.01/1.26 % ------ iProver source info
% 3.01/1.26
% 3.01/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.01/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.01/1.26 % git: non_committed_changes: false
% 3.01/1.26
% 3.01/1.26 % ------ Parsing...
% 3.01/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.01/1.26
% 3.01/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.01/1.26
% 3.01/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.01/1.26
% 3.01/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.01/1.26 % ------ Proving...
% 3.01/1.26 % ------ Problem Properties
% 3.01/1.26
% 3.01/1.26 %
% 3.01/1.26 % clauses 18
% 3.01/1.26 % conjectures 1
% 3.01/1.26 % EPR 4
% 3.01/1.26 % Horn 15
% 3.01/1.26 % unary 6
% 3.01/1.26 % binary 6
% 3.01/1.26 % lits 36
% 3.01/1.26 % lits eq 8
% 3.01/1.26 % fd_pure 0
% 3.01/1.26 % fd_pseudo 0
% 3.01/1.26 % fd_cond 0
% 3.01/1.26 % fd_pseudo_cond 3
% 3.01/1.26 % AC symbols 0
% 3.01/1.26
% 3.01/1.26 % ------ Schedule dynamic 5 is on
% 3.01/1.26
% 3.01/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.01/1.26
% 3.01/1.26
% 3.01/1.26 % ------
% 3.01/1.26 % Current options:
% 3.01/1.26 % ------
% 3.01/1.26
% 3.01/1.26
% 3.01/1.26 %
% 3.01/1.26
% 3.01/1.26 % ------ Proving...
% 3.01/1.26 %
% 3.01/1.26
% 3.01/1.26 % SZS status Theorem for theBenchmark.p
% 3.01/1.26
% 3.01/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.01/1.26
% 3.01/1.26
%------------------------------------------------------------------------------